Context. Due to their nearly constant absolute magnitudes and old ages, blue horizontal branch (BHB) stars are frequently used as standard candles to study the kinematics and structures of our galaxy. The number of identified BHB stars has significantly increased due to the advent of large scale surveys in the last two decades. Recently, Gaia DR3 was released including a catalog of around 220 million low-resolution spectra (Bp/Rp, or XP hereafter). These data have great potential for identifying many interesting stellar objects including BHB stars. Aims. We construct a full-sky BHB catalog from Gaia Bp/Rp spectra and use it to explore the shape of the inner stellar halo. Methods. We selected BHB stars based on synthetic photometry and stellar atmosphere parameters inferred from Gaia Bp/Rp spectra. We generated the synthetic SDSS broad-band ugr and Pristine narrow-band CaHK magnitudes from Gaia Bp/Rp data. A photometric selection of BHB candidates was made in the (u ‑ g, g ‑ r) and (u ‑ CaHK, g ‑ r) color-color spaces. A spectroscopic selection in Teff ‑ log g space was applied to remove stars with high surface gravity. The selection function of BHB stars was obtained by using the Gaia DR3 photometry. A non-parametric method that allows the variation in the vertical flattening q with the Galactic radius, was adopted to explore the density shape of the stellar halo. Results. We present a catalog of 44 552 high latitude (|b| > 20°) BHB candidates chosen with a well-characterized selection function. The stellar halo traced by these BHB stars is more flattened at smaller radii (q = 0.4 at r ~ 8 kpc), and becomes nearly spherical at larger radii (q = 0.8 at r ~ 25 kpc). Assuming a variable flattening and excluding several obvious outliers that might be related to the halo substructures or contaminants, we obtain a smooth and consistent relationship between r and q, and the density profile is best fit with by a single power law with an index α = ‑4.65 ± 0.04.